Using software developed at the Cockrell School of Engineering and a low-cost GPS antenna, students in professor Todd Humphreys' Radionavigation Lab demonstrate position tracking of a virtual reality headset to centimeter accuracy, in real time.
Researchers in the Cockrell School of Engineering at The University of Texas at Austin have developed a centimeter-accurate GPS-based positioning system that could revolutionize geolocation on virtual reality headsets, cellphones and other technologies, making global positioning and orientation far more precise than what is currently available on a mobile device.
The researchers’ new system could allow unmanned aerial vehicles to deliver packages to a specific spot on a consumer’s back porch, enable collision avoidance technologies on cars and allow virtual reality (VR) headsets to be used outdoors.
The researchers’ new centimeter-accurate GPS coupled with a smartphone camera could be used to quickly build a globally referenced 3-D map of one’s surroundings that would greatly expand the radius of a VR game.
Currently, VR does not use GPS, which limits its use to indoors and usually a two- to three-foot radius.
“Imagine games where, rather than sit in front of a monitor and play, you are in your backyard actually running around with other players,” said Todd Humphreys, assistant professor in the Department of Aerospace Engineering and Engineering Mechanics and lead researcher.
“To be able to do this type of outdoor, multiplayer virtual reality game, you need highly accurate position and orientation that is tied to a global reference frame.”
Humphreys and his team in the Radionavigation Lab have built a low-cost system that reduces location errors from the size of a large car to the size of a nickel — a more than 100 times increase in accuracy.
Humphreys collaborated with Professor Robert W. Heath from the Department of Electrical and Computer Engineering and graduate students on the new technology, which they describe in a recent issue of GPS World.
Centimeter-accurate positioning systems are already used in geology, surveying and mapping, but the survey-grade antennas these systems employ are too large and costly for use in mobile devices.
The breakthrough by Humphreys and his team is a powerful and sensitive software-defined GPS receiver that can extract centimeter accuracies from the inexpensive antennas found in mobile devices — such precise measurements were not previously possible.
The researchers anticipate that their software’s ability to leverage low-cost antennas will reduce the overall cost of centimeter accuracy, making it economically feasible for mobile devices.
Humphreys and his team have spent six years building a specialized receiver, called GRID, to extract so-called carrier phase measurements from low-cost antennas.
GRID currently operates outside the phone, but it will eventually run on the phone’s internal processor.
To further develop this technology, Humphreys and his students recently co-founded a startup, called Radiosense.
Humphreys and his team are working with Samsung to develop a snap-on accessory that will tell smartphones, tablets and virtual reality headsets their precise position and orientation.
The researchers designed their system to deliver precise position and orientation information — how one’s head rotates or tilts — to less than one degree of measurement accuracy.
This level of accuracy could enhance VR environments that are based on real-world settings, as well as improve other applications, including visualization and 3-D mapping.
Additionally, the researchers believe their technology could make a significant difference in people’s daily lives, including transportation, where centimeter-accurate GPS could lead to better vehicle-to-vehicle communication technology.
“If your car knows in real time the precise position and velocity of an approaching car that is blocked from view by other traffic, your car can plan ahead to avoid a collision,” Humphreys said.
Samsung provided funding to Humphreys’ Radionavigation Lab at UT Austin for the centimeter-accurate global positioning system research and plans to continue funding related basic research.
A team of German and Canadian researchers have discovered
areas with extremely low levels of oxygen in the tropical North
Atlantic, several hundred kilometres off the coast of West Africa. The
levels measured in these ‘dead zones’, inhabitable for most marine
animals, are the lowest ever recorded in Atlantic open waters. The dead
zones are created in eddies, large swirling masses of water that slowly
move westward. Encountering an island, they could potentially lead to
mass fish kills. The research is published today in Biogeosciences, an open access journal of the European Geosciences Union (EGU).
Dead zones are areas of the ocean depleted of oxygen.
Most marine
animals, like fish and crabs, cannot live within these regions, where
only certain microorganisms can survive.
In addition to the
environmental impact, dead zones are an economic concern for commercial
fishing, with very low oxygen concentrations having been linked to
reduced fish yields in the Baltic Sea and other parts of the world.
Red circles show the location and size of many dead zones. Black dots show dead zones of unknown size. The size and number of marine dead zones—areas where the deep water is so low in dissolved oxygen that sea creatures can't survive—have grown explosively in the past half-century.
Robert Simmon & Jesse Allen - NASA Earth Observatory
“Before our study, it was thought that the open waters of the North
Atlantic had minimum oxygen concentrations of about 40 micromol per
litre of seawater, or about one millilitre of dissolved oxygen per litre
of seawater,” says lead-author Johannes Karstensen, a researcher at GEOMAR,
the Helmholtz Centre for Ocean Research Kiel, in Kiel, Germany.
This
concentration of oxygen is low, but still allows most fish to survive.
In contrast, the minimum levels of oxygen now measured are some 20 times
lower than the previous minimum, making the dead zones nearly void of
all oxygen and unsuitable for most marine animals.
Dead zones are most common near inhabited coastlines where rivers
often carry fertilisers and other chemical nutrients into the ocean,
triggering algae blooms.
As the algae die, they sink to the seafloor and
are decomposed by bacteria, which use up oxygen in this process.
Currents in the ocean can carry these low-oxygen waters away from the
coast, but a dead zone forming in the open ocean had not yet been
discovered.
The newly discovered dead zones are unique in that they form within
eddies, large masses of water spinning in a whirlpool pattern.
“The few
eddies we observed in greater detail may be thought of as rotating
cylinders of 100 to 150 km in diameter and a height of several hundred
metres, with the dead zone taking up the upper 100 metres or so,”
explains Karstensen.
The area around the dead-zone eddies remains rich
in oxygen.
“The fast rotation of the eddies makes it very difficult to exchange
oxygen across the boundary between the rotating current and the
surrounding ocean.
Moreover, the circulation creates a very shallow
layer – of a few tens of meters – on top of the swirling water that
supports intense plant growth,” explains Karstensen.
This plant growth
is similar to the algae blooms occurring in coastal areas, with bacteria
in the deeper waters consuming the available oxygen as they decompose
the sinking plant matter.
“From our measurements, we estimated that the
oxygen consumption within the eddies is some five times larger than in
normal ocean conditions.”
The eddies studied in the Biogeosciences
article form where a current that flows along the West African coast
becomes unstable.
They then move slowly to the west, for many months,
due to the Earth’s rotation.
“Depending on factors such as the [eddies’]
speed of rotation and the plant growth, the initially fairly oxygenated
waters get more and more depleted and the dead zones evolve within the
eddies,” explains Karstensen.
The team reports concentrations ranging
from close to no oxygen to no more than 0.3 millilitres of oxygen per
litre of seawater.
These values are all the more dramatic when compared
to the levels of oxygen at shallow depths just outside the eddies, which
can be up to 100 times higher than those within.
Dead zone in the Gulf of Mexico :
the difference between hypoxic water (murky green) and well-oxygenated water (clear blue).
The researchers have been conducting observations in the region off
the West African coast and around the Cape Verde Islands for the past
seven years, measuring not only oxygen concentrations in the ocean but
also water movements, temperature and salinity.
To study the dead zones,
they used several tools, including drifting floats that often got
trapped within the eddies.
To measure plant growth, they used satellite
observations of ocean surface colour.
Their observations allowed them to measure the properties of the
dead zones, as well as study their impact in the ecosystem. Zooplankton –
small animals that play an important role in marine food webs – usually
come up to the surface at night to feed on plants and hide in the
deeper, dark waters during the day to escape predators.
However, within
the eddies, the researchers noticed that zooplankton remained at the
surface, even during the day, not entering the low-oxygen environment
underneath.
“Another aspect related to the ecosystem impact has a socioeconomic
dimension,” says Karstensen. “Given that the few dead zones we observed
propagated less than 100 km north of the Cape Verde archipelago, it is
not unlikely that an open-ocean dead zone will hit the islands at some
point. This could cause the coast to be flooded with low-oxygen water,
which may put severe stress on the coastal ecosystems and may even
provoke fish kills and the die-off of other marine life.”
Scientists tracking Gulf sparrows, insects, and seabirds try to unravel the mysteries of a landscape changed by oil.
Every spring, scientists tromp through Louisiana's mud and waist-high grass, hunting for the hidden nests of a palm-size bird called the seaside sparrow.
Their goal: to see whether the massive oil spill from a broken Gulf of Mexico rig known as Deepwater Horizon has hurt creatures that don't actually inhabit the water.
Five years after the worst oil spill in U.S. history, early reports from this and other research suggest that the ecological damage lingered in unexpected ways.
But scientists say cataloging what that means for the Gulf's future grows more complex with time.
Amid the rushes and cordgrass of the Gulf's fragile salt marshes, for example, scientists say they made a surprising discovery: Two years after the spill, in meadows once tarnished by soupy petroleum, flies, crickets, spiders, and the seaside sparrows that eat them were less abundant than in areas untouched by the oil.
"There's very little question that our oiled plots had greatly reduced sparrow densities," saysStefan Woltmann, an assistant professor of biology with Austin Peay State University in Tennessee.
"Nest success was miserable out there."
Many of these marsh creatures never came in contact with spilled crude, so the connections between the oil spill and their fate are poorly understood.
Some scientists suspect that insects important to wildlife were snuffed out by oily residue that released toxic fumes.
Smoke rises from oil burned by cleanup crews near the Deepwater Horizon rig on April 20, 2010. Five years later, scientists are still trying to unravel how the largest oil spill in U.S. history affected wildlife in the Gulf of Mexico.
Photograph by Joel Sartore, National Geographic Creative
The effects on seaside sparrows, a ubiquitous symbol of salt marshes from Texas to Florida, appear to have been localized and temporary.
But despite the region's apparent resilience, scientists say they don't yet know how much these coastal wetlands—important nurseries for fish and feeding grounds for birds—are still changing in subtle ways.
In addition, some research suggests that the spill may still be harming ocean creatures, such as bottlenose dolphins, killifish, and corals.
"The spill was a terrible experiment over a huge landscape with a sample size of one, and we're basically in the audience, watching," saysLinda Hooper-Bùi, an entomologist with Louisiana State University.
BP, which owned and operated the well that suffered the blowout on April 20, 2010, stated in a report last month that there has been no population-scale decline inany Gulf species.
The report says data collected by independent scientists in 2011 showed no differences in survival of six bird species, including seaside sparrows, between oiled and unoiled areas.
"The dire predictions made in 2010 have fortunately not come to pass," the report states.
But officials representing the Gulf states and the U.S. government, which are suing BP to recover money for ecological restoration, dismiss the BP report as"inappropriate and premature"and say it "misinterprets and misapplies data."
As with virtually everything connected to the 2010 accident, scientists say it's simply too early to tell about the long-term damage.
A dead juvenile sea turtle was marooned in oil in Barataria Bay, Louisiana, in June, 2010. Photograph by Joel Sartore, National Geographic Creative
"Like an Underwater Dust Storm"
It was a slow-moving disaster unlike any other.
The nighttime explosion on Deepwater Horizonkilled 11 workers and injured many others.
BP spent 87 days trying to cap the leaking wellhead before finally halting the oil's flow.
By then, more than100 million gallonshad escaped.
Squiggly ribbons of red-brown goo coated the Gulf.
"I remember it like it was yesterday: It looked like an underwater Oklahoma dust storm," recallsP. J. Hahn, then director of coastal zone management for Louisiana's Plaquemines Parish.
"We'd fly over it, and you could see there was more oil traveling below than above the water. We'd dive in it and see oil from horizon to horizon. It was overwhelming. It was heartbreaking."
Chocolate-colored glop coated hermit crabs, fiddler crabs, pelicans, and terns and formed thick, oily mats that carried sea turtles.
(Some600 turtles died; BP suggests many weren't killed by oil.)
Crude darkened white sand beaches, coated mangroves, and washed ashore carrying dead dolphins and fish.
Shrimp and oyster harvesting was temporarily scuttled. Lesions appeared on the skin of red snappers.
Seabirds were the most visible victims.
Roughly 6,000 birds were found dead that first year, mostly laughing gulls, pelicans, and northern gannets.
BP contends that most bird carcasses were found, but the U.S. Fish and Wildlife Service suspects that number is a fraction of actual spill-related bird deaths.
Five years later, in many ways, much appears to be back to normal.
Oily tar is rarely seen in the marsh; most of it was consumed by oil-eating microbes.
Fish lesions are no longer common.
Commercial fish landings are up.
"Generally speaking, a great deal of the oil has been degraded,"says Ed Overton, an emeritus professor of environmental chemistry at Louisiana State.
"There's not anywhere close to as much detectable oil."
But published research suggests the BP spill hurt wildlife in countless ways, contributing to a mass die-off ofdolphins,potentially harming the hearts of baby tuna, anddamaging killifishDNA.
BP is critical of these studies, arguing, in part, that dolphin die-offs are common and that their deaths may seem more frequent because more people are paying attention.
The company, in a statement, also said fish research "provides no evidence to suggest a population-level impact on tuna or other fish species in the Gulf of Mexico."
But some research suggests spill-related problems will keepechoingand ultimately could harmanimal immune systems, reproduction andspecies'range.
Other studies are still ongoing or tied up in court proceedings that will determine how much BP will pay for environmental damage.
And because the spill hit marine and estuarine systems already facing pollution and erosion, it is difficult to document changes and isolate causes.
To understand just how complex that is, consider the efforts to track sparrows and their food
Did Oil Harm Sparrows?
Seaside sparrows nest low in high grass and, unlike migrating waterfowl, spend their entire lives in Gulf marshes.
That makes these tiny brown and gray birds a good indicator of the health of these ecosystems.
Gulf marshes have been disappearing and degraded for decades.
Some urban areas lost 85 percent in the last century because of dredging, flooding, development, and rising seas.
Then the oil spill soiled more than 1,100 miles (1,700 kilometers) of shoreline, much of it marsh in southeastern Louisiana's Barataria Bay.
Some wetlands were so plastered with oil thatvegetation died.
Grasses were still spotty years later, scientists say, and some plant speciesrecovered poorly.
The oil may have left marshes more vulnerable to erosion.
In 2012, the bird researchers found "more birds on unoiled sites, more nests on unoiled sites, and greater reproductive success on unoiled sites" than on oiled sites, says Louisiana State University ecologistSabrina Taylor.
The researchers are uncertain what these unpublished findings, which have not been reviewed by outside scientists, mean for sparrows.
And they have not documented the same pattern since 2012.
"It could be that those birds are having to deal with processing and metabolizing contaminants," Taylor says.
"It could be that the sediment was degraded, that the marsh grass isn't doing as well. If the grass is sparser their nests might not be as camouflaged."
Or sparrows might have worked harder to find food.
Where'd the Bugs Go?
In September 2010, insect expert Hooper-Bùi and her team checked the marsh for katydids, crickets, spiders, and seed bugs—staples of the sparrow diet.
"Insects were radically suppressed," she says.
The next spring her team returned, expecting a resurgence, asother researchersstudying marsh snails and other crabs had seen.
But things were worse.
Cat Island, a barrier island and nesting spot for brown pelicans in
Barataria Bay near Grand Isle, Louisiana, was protected with inflatable
booms after the oil spill in 2010.
Time lapse of Google Earth photos starting from 1998 to Present. Exacerbated due to the BP Deepwater Horizon Oil spill, the marsh damage hastened the barrier island's erosion. The lingering oil impacted the already-delicate vegetation and now the pelicans' nesting area has disappeared. The date is in the lower left corner.
The island is now almost entirely underwater, and some scientists suspect that oil killed its mangroves, speeding erosion. Photograph by Joel Sartore, National Geographic Creative
"It was actually devastating to see," she says.
"We're sampling [for insects] in the green grass behind the oiled zone, and we're coming out with nothing in our net."
Chemists had suggested oil would have weathered, biodegraded, or been stripped of most toxic components before reaching the marsh.
But scientists late last year discovered that chemicals in oil known as PAHs (polycyclic aromatic hydrocarbons) are still high and mightstick aroundfor many years.
To find out what happened to the insects, Hooper-Bùi built cages.
When the tide was low, the insects sat in them on the ground.
When it was high, the cages floated.
Oily compounds could only reach bugs through air.
When temperatures hit 85 degrees Fahrenheit, "volatile compounds came off the sediments and killed the insects in the cages," Hooper-Bùi says.
Insects on unoiled sites survived.
She repeated the test in an incubator and in her backyard.
Each time, insects exposed to oil compounds died when temperatures rose.
"We have some strong, indirect evidence that something's happening but we don't know what," she says.
Hooper-Bùi's findings have not been published, and BP officials declined to comment on her results because they had not seen her data.
Ants migrated back into oiled areas in 2012, but she says by midsummer they had died or begun starving.
Then in August of that year, Hurricane Isaac blew in, potentially spreading old oil to new sites, complicating everything more.
"A storm event or high tides or hurricanes will reemerge that buried oil and spread it around," says Overton, the chemist.
"That's going to keep going on until all that oil is gone."
It's possible some of the oil came from natural seeps unrelated to the spill or other sources.
During the next year, Hooper-Bùi says she watched unoiled sites repair themselves after the hurricane, while oiled sites struggled.
There were fewer insects, and many of them vanished again when it turned hot in July. Jill Olin, a postdoctoral researcher at Stony Brook University who analyzed sparrow liver and stomach contents, says the spill did not seem to alter what sparrows ate.
But it might have changed how they hunted for their food, which could "ultimately affect fitness and nesting success."
P. J. Hahn, a former Plaquemines Parish official, rescued an oil-covered brown pelican on Queen Bess Island, Louisiana, in 2010. Hahn remembers those first few weeks after the spill as "overwhelming" and "heartbreaking."
Photograph by Joel Sartore, National Geographic Creative
Loons and Pelicans Affected
Related questions trail other birds, too.
Brown pelicans, Louisiana's state bird, all but vanished a half-century ago before staging a comeback after the pesticide DDT was banned in 1972.
Many pelicans nested on barrier islands that were slathered by Deepwater Horizon oil.
Two spits, together known as Cat Island, have eroded to silhouettes below water, possibly because the oil killed the roots of island-stabilizing mangroves.
The island was eroding already, "but the spill accelerated the land loss," says Gene Turner, a Louisiana State oceanography professor.
So where have Cat Island's pelicans gone?
No one knows.
BP points to a study that found no major issues with brown pelicans.
The authors, however, say their findings don't rule out future problems.
Meanwhile, scientists have found hydrocarbons in the eggs of American white pelicans as far north as Minnesota as well as in the eggs, blood, and feathers of loons.
Researchers haven't definitively linked the chemicals to the BP spill, but samples contained residue from dispersants used in the Gulf cleanup.
BP officials contend the compounds could be from hydrocarbons found naturally in the environment or from other sources.
Minnesota officials disagree.
"There's just really no other place it would have come from except theDeepwater Horizon event," says Carrol Henderson, Minnesota's nongame wildlife program supervisor.
In Louisiana, PAH levels in the blood of Gulf loons were higher several years after the spill than in the immediate aftermath.
Again, no one has figured out why.
"The levels were potentially high enough to be causing sublethal effects"—impacts that could affect the birds' longevity or reproduction, says Jim Paruk, with the Biodiversity Research Institute in Maine.
Understanding the ecological toll of the spill ultimately may take decades.
Scientists still don't fully understand why some species declined in the wake of the Exxon Valdez spill in Alaska 26 years ago.
Are the Gulf of Mexico marshes more resilient than Alaska's Prince William Sound?
"We don't know yet," Woltmann says. That's why scientists "continue to explore ways that this spill might impact wildlife in less obvious ways."
The illegal seizure of the Maersk Tigris illustrates Tehran’s desire to pick and choose what international rules it follows.
Iran’s seizure of the MV Maersk Tigris underscores the importance of a stable rule of law in the oceans, and the dangers of allowing one state to attempt to alter them for its own benefit.
MV Maersk Tigris
The ship, boarded and taken by force to Bandar Abbas on April 28, was turned over to the Iranian Revolutionary Guard to fulfill a court judgment in favor of Iran Ports Authority.
It should surprise no one that this vacuous legal rationale is incompatible with the the rules set forth in the customary international law of the sea, and reflected in the Law of the Sea Convention, or LOSC.
The Strait of Hormuz is 21 nautical miles in width, and constitutes the territorial sea of Oman and Iran.
The Maersk Tigris, sailing under the flag of the Republic of the Marshall Islands, was captured in the Strait in an area overlapped by Iranian territorial waters.
Under the LOSC, the parts of the territorial sea that are used for navigation and that connect one area of the high seas or exclusive economic zone (EEZ), in this case the Persian Gulf, with another area of the high seas or EEZ, here the Arabian Sea, form a strait used for international navigation.
Straits have a dual nature, as they are simultaneously territorial seas of the affected coastal states as well as strait used for international navigation.
As a reminder the Straight of Ormuzis one of the busiest shipping lanes in the world, one which is transited by 35% of all seaborne traded oil. First East Traffic Separation Scheme (TSS) and Western TSS with the Marine GeoGarage
The regime of transit passage applies in such straits, and Maersk Tigris enjoyed unimpeded transit through the strait.
Unlike in innocent passage, submarines may travel submerged and aircraft may overfly the strait while in transit passage.
Notwithstanding the regime of transit passage, article 42 ofUNCLOS authorizes the coastal state to adopt laws for regulation of commercial maritime traffic, vessel discharge of oil, prevention of illegal fishing, and customs and immigration matters.
With the limited exception for violations that may cause or threaten to cause “major damage” to the marine environment of the strait, Iran may not enforce its laws against foreign flag vessels transiting the strait.
In any case, such laws cannot have the “practical effect of denying, hampering, or impairing the right of transit passage.”
Outside of straits, navigation in the territorial sea must be in innocent passage.
Only surface ships and submarines transiting on the surface enjoy the right. Article 28(2) of theLOSC states that the coastal state may not arrest a foreign ship for any civil proceeding, except for liabilities incurred by the ship itself, and then only during the course of or for the purpose of the specific transit.
Iran has signed, but not ratified the LOSC. As a signatory to the treaty, however, Tehran is obligated not to undermine its “object and purpose.”
(This responsibility is set forth in the Vienna Convention on the Law of Treaties.)
The essential bargain in the LOSC was expansion of the customary territorial sea from 3 nautical miles to 12 in exchange for the recognition of the right of transit passage through straits. Yet Iran claimsthat the terms of the treaty are “merely a product of quid pro quo,” and therefore nonparties to the treaty, such as the United States, do not enjoy the right of transit passage.
The United States counters that although the regime of transit passage through straits is reflected in LOSC, it springs from customary international law and is therefore already binding on all states.
The legal right of passage through the Strait of Hormuz is tied to the collateral issue of the width of the territorial sea of Iran and Oman.
If Iran expands its territorial sea from the 3 miles to 12, it must accept transit passage as part of the overall package deal.
If there is no transit passage in the Iranian territorial sea, then Iran is permitted to claim only a 3-mile territorial sea.
High seas freedoms would apply beyond that limit.
Speedboats of Iran’s Islamic Revolution Guards Corps (IRGC) are seen during major drills in the Strait of Hormuz in the Persian Gulf code-named the Great Prophet 9 on February 25, 2015.
Iran’s current claim of a 12-mile territorial sea means that other nations are entitled to exercise freedom of navigation and enjoy transit passage through the strait.
Otherwise, ships and aircraft would still have a right to the historic antecedent of general high seas freedoms, which is even more permissive.
Either way, the law of the sea recognizes unimpeded passage. Instead, Iran has sought to preserve the navigational regime of innocent passage.
Expansion of Territorial waters in the Straight of Hormuz
Even assuming that the regime of innocent passage applied to the Maersk Tigris, however, Iran’s seizure was still unlawful.
Tehran is trying to replace the package deal of the law of the sea with a cafeteria-style selection of favored provisions and rejection of others that benefit and protect the international community.
This conduct is of a familiar style and pattern for the regime in Iran, and an indictment on its ability to implement international law in good faith.
David Cooke said he discovered the longest land to land 'straight line' ocean route on Earth. Over 2000 miles longer than the one from Kamchatka to Pakistan. Really ?
Timothy Whitehead from Google Earth blog recently came across this post on Reddit.
It references to the above YouTube video
from David Cooke, claiming to have discovered the longest straight line that can be
sailed without going over land.
The video creator calls it the "Cooke Passage".
However, we have attempted to recreate it in Google Earth, and it appears that it is not actually a straight line.
GoogleMapsMania has in the past discussed what constitutes a straight line in Google Earth.
In this instance, we are interested in Great Circles,
which is what Google Earth uses by default when drawing a path.
However, Google Earth always draws the shorter arc of a Great Circle, so
to draw the longer section of a Great Circle it is necessary to include
at least one more point and then adjust it with care.
You know you have
got it right if you can draw another shorter path on any section of it
and it still follows the same path.
Using the above techniques, and locations shown in the video, we have
investigated the Cooke Passage and decided that it does not follow a
great circle.
We also confirm this statement and in order to go further in analyzing this route, we propose a more accurate method for drawing the longer section of a Great Circle (orthodromic route) on Google Earth :
Note : Great-circle navigation is the practice of navigating a ship along a great circle (shortest route).
A great circle track is the shortest distance between two points on the surface of a sphere; the Earth isn't exactly spherical, but the formulas for a sphere are simpler and are often accurate enough for navigation.
1/ calculate the Great Circle route from the Start point to the End point :
in this
Cooke passage case :
. start : near Port Cartier, Quebec : 49°52'9" N
/ 67°0'0" W (49.86916667/-67 in decimal)
. end : Port Renfrew, Victoria BC : 48°35'34,34" N / 124°43'48" W (48.59287222/-124.73 in decimal)
Minor Arc Great circle on Google Maps (2,214.33 Nm GC / 2,269.52 Nm Rhumb Line)
initial bearing : 290.9° from East to West
As the long arc is higher than half of the Earth circumference at the Equator (so higher than 10,819 Nm, actually in this case about 19,401 Nm), the calculation will give the shorter arc of the Great Circle.
Effectively, points A and B split their great circle in two arcs of which (except for antipodal A and B) one is shorter than the other. The important bit is that the calculation of the shortest distance between two points on a sphere is done for the minor arc of a Great Circle.
Then how to calculate the major arc ?
2/ calculating at first the midpoint of this minor arc (the half-way point along a great circle path between the two points) using the ‘Haversine’ formula.
Cook passage (minor arc Great Circle) midpoint :52.9425/-95.72694444
on Google Maps (Mercator projection)
3/ then calculating the antipodal of the midpoint for this minor arc which represents the midpoint of the major arc :
Given a point on a sphere with latitude and longitude, the antipodal point has latitude -Lat and longitude Lon+/-180 degrees (where the sign is taken so that the result is between -180 degrees and +180 degrees).
Cook passage (minor arc) antipodal midpoint in the South of the Indian ocean
Map tunneling tool : -Lat/180+Lon so -52.9425/84.27305556
This point will be the necessary intermediate waypoint allowing to draw the major arc Great Circle with Google Earth : see the resulting kml file.
and the Cooke passage Great Circle major Arc on Google Earth showing the line crossing Australia, so not a new world longest GC straight-line sail :
By the way, to follow a great circle track, the navigator needs to adjust the
ship's course continuously because the great circle track is a curve
when plotted on a Mercator map (see illustration above).
Therefore, it is not really practicable to sail on an exact Great Circle route.
In
order to take advantage of the shorter distance given by the Great Circle track, mariners usually divide a Great Circle track between the
initial position and the destination into smaller segments (way points)
corresponding to some sailing time and make course adjustments at each
next waypoint.
The total distance is therefore the sum of the distances of those rhumb line segments (loxodromic with constant angle route) calculated by means of Napier rules for spherical triangles, allowing to calculate several individual waypoint's WGS84 Latitude and Longitude.
In some previous GeoGarage posts regarding longest GC sailing :
we can apply the above method -using the antipodal of the midpoint for this minor arc- and also calculate the Great Circle major Arc waypoints with other intermediates (for example a serie of waypoints at x Nm of distance)
Pakistan-Siberia.kml route on Google Maps (straight on the Google Earth globe) : real Great Circle corrected by the GeoGarage team (about 32,105 km/17,335 Nm) not crossing Aldabra and Assumption island in the North West of Madagascar.
&Pakistan-Siberia_WPTS.kmzbuilt with 1731 intermediate waypoints every 10 Nm (note some difference with the above Pakistan-Siberia.kml route due to different GC calculations)
GoogleMapsMania also came across another interesting, though shorter route that goes from Norway to Antarctica by way of the Bering Strait.
GoogleMapsMania : Various routes (kml file) including Norway-Antarctica route
Using an intermediate waypoint as the antipodal of the midpoint for this minor arc between Norway and Antarctica, passing by the Bering straight, we get a different result comparing to the above kml file issued from GoogleMapsMania.
crossing Saint Lawrence island in the Bring Strait
But another factor to take into consideration is the location of the vertex, or the point of greatest latitude through which the circle passes. In this case, the route mainly crosses the North pole area. So this is not a realistic sailing route, by the way some Composite Great Circle with limited Latitude can't be used. Note : when using a Composite Great Circle track, a limiting Latitude is chosen, beyond which the vessel does no go. When the limiting latitude is reached the vessel then sails either due East or West on the limiting Latitude as in parallel sailing. In order to reach the limiting Latitude, the vessel follows an appropriate Great Circle track whose vertex lies on the limiting Latitude.
